Wetlands are the largest global source of atmospheric methane (CH4)(1), a potent greenhouse gas. However, methane emission inventories from the Amazon floodplain(2,3), the largest natural geographic source of CH4 in the tropics, consistently underestimate the atmospheric burden of CH4 determined via remote sensing and inversion modelling(4,5), pointing to a major gap in our understanding of the contribution of these ecosystems to CH4 emissions. Here we report CH4 fluxes from the stems of 2,357 individual Amazonian floodplain trees from 13 locations across the central Amazon basin. We find that escape of soil gas through wetland trees is the dominant source of regional CH4 emissions. Methane fluxes from Amazon tree stems were up to 200 times larger than emissions reported for temperate wet forests(6) and tropical peat swamp forests(7), representing the largest non-ebullitive wetland fluxes observed. Emissions from trees had an average stable carbon isotope value (delta C-13) of -66.2 +/- 6.4 per mil, consistent with a soil biogenic origin. We estimate that floodplain trees emit 15.1 +/- 1.8 to 21.2 +/- 2.5 teragrams of CH4 a year, in addition to the 20.5 +/- 5.3 teragrams a year emitted regionally from other sources. Furthermore, we provide a 'topdown' regional estimate of CH4 emissions of 42.7 +/- 5.6 teragrams of CH4 a year for the Amazon basin, based on regular vertical lower-troposphere CH4 profiles covering the period 2010-2013. We find close agreement between our 'top-down' and combined 'bottom-up' estimates, indicating that large CH4 emissions from trees adapted to permanent or seasonal inundation can account for the emission source that is required to close the Amazon CH4 budget. Our findings demonstrate the importance of tree stem surfaces in mediating approximately half of all wetland CH4 emissions in the Amazon floodplain, a region that represents up to one-third of the global wetland CH4 source when trees are combined with other emission sources.